Saturday, July 23, 2011

Failure of a simple weighted mean algorithm

I will demonstrate this with an example. The thing that I was trying to do was to make the distances exactly proportional to the edge lengths. This is not possible always.

Take a very simple example in 2D, i.e a plane.

Suppose you have 4 points A,B,C and D on the plane and you want to find out a point such that the distances of these points from that central point is in the same proportions.
It is very easy to see that this is not always possible. Well to start you can choose any 3 points and draw a circle through them but now you got yourself in a problem. It is not necessary that D is also concyclic to the same circle.
Further things in spherical geometry make things even worse.

I need some other idea to use/represent this information. Had it been an animation then things would have been different.